Analysis, Modeling, and Characterization of Solar Cells
Raul Mittmann Reis and Sergey Edward Lyshevski
Department of Electrical and Microelectronic Engineering
Rochester Institute of Technology
Rochester, NY 14623 USA
E-mail: [email protected]
URL: http://people.rit.edu/seleee www.rit.edu/kgcoe/staff/sergey-lyshevski
ABSTRACT
Energy harvesting, energy storage and energy
management are of a significant importance in biomedical
devices, cell phones, computers and tablets, consumer
electronics, communication, security, micro aerial vehicles,
etc. In many applications, solar cells and photovoltaic
modules may guarantee autonomy, sustainability, energy
adequateness, etc. In this paper, experimental results for
mini-solar cell are performed, models are parametrized and
parameters are found. Our findings are substantiated.
Keywords: photovoltaics, solar cell, parameter estimation
1. INTRODUCTION
For different applications, single- and multi-junction
solar cells are fabricated using polycrystalline and
monocrystalline silicon, amorphous and nanocrystalline
silicon, cadmium telluride, copper indium gallium selenide,
gallium arsenide and other materials. Quantum dots (CdS,
CdSe, PbS, Sb2S and others), organic and polymer solar
cells are also used in some applications. This paper
examines commercial polycrystalline and amorphous
silicon solar cells which ensure cost effectiveness,
sufficient power density, adequate efficiency (up to ~15%),
stability and robustness.
We study the application of solar cells for self-
sustained biomedical, electronic and MEMS devices, as
well power systems [1, 2]. The top n- and bottom p-type
phosphorus and boron doped layers form the pn junction
with a strong electrical field across. When photons are
absorbed, the photocurrent is generated due to a flow of
electrons. The solar cells and modules can be packaged
using waterproof and transparent material. A wide spectrum
of application of photovoltaic modules and solar cells is
under consideration [3].
2. SOLAR CELLS
In solar cells, the absorption of photons results in
generation of the charge carriers (electrons), and,
subsequent separation of the photo-generated charge
carriers. In crystalline silicon (c-Si) solar cells, there are
two doped top n+ and back p+ layers. The performance of
solar cells depends on: (1) Concentrations ND and NA of
doping atoms which determine the width of a p-n junction
space-charge region (donor atoms donate free electrons,
while acceptor atoms accept electrons); (2) Mobility of
electrons µn and holes µp; (3) Diffusion coefficient D which
characterizes the charge carriers transport due to drift and
diffusion; (4) Lifetime τ and diffusion length L of the
excess carriers which characterize recombination-
generation; (5) Band gap energy Eg, absorption coefficient
α and refractive index R which characterize photon
absorption. Usually, the output voltage of an individual c-Si
cell is ~0.5V. The images of the examined crystalline and
amorphous silicon solar cells are reported in Figure 1.
Figure 1. Images of Si solar cells
We perform experimental studies and derive high-
fidelity, descriptive and physics-consistent models of solar
cells. The solar cells are tested and characterized to justify
results. Using the experimental I–V and P–V characteristics,
the solar cell parameters are determined. The experimental
and calculated I–V and P–V characteristics should be
consistent. The I–V and P–V characteristics are measured
under the standard temperature and irradiance. Our goal is
to perform a consistent characterization, analysis, modeling,
simulation and evaluation which can be applied to design of
commercial power sources for self-sustained and portable
systems.
3. ANALYSIS OF SOLAR CELLS
Performance and capabilities of photovoltaic modules
and solar cells are technology- and design dependent. The
output of an individual c-Si cell is usually ~0.5V. The
efficiency of c-Si solar cell is estimated as η=Pmax/GA,
Materials for Energy, Efficiency and Sustainability: TechConnect Briefs 2016 27
where Pmax is the maximum power point; G is the irradiance
in W/m2; A is the surface area in m
2.
The experimental and analytic I–V and P–V
characteristics are studied. The solar cell equivalent circuit
is depicted at Figure 2 [3, 4].
Ipv
ID RpG(t)+
–
D
Rs
Iph
Vpv
Figure 2. Single diode solar cell model
Using a conventional model [3, 4], the current Ipv is
p
spvpv
DphpvR
RIVIII
+−−= , (1)
where Iph is the photo current due to irradiation G; ID is the
diode current; Rs is the series resistance; Rp is the shunt
resistance, Rp>>Rs.
For the diode current ID, we have
)1(0 −=
+
ta
spvpv
aV
RIV
D eII , (2)
where a is the diode quality coefficient (1< a <2, for a large
forward-bias voltage, a is ~1 or ~2 when diffusion or
recombination dominate, respectively); Vta is the thermal
voltage, q
kTNV s
ta = ; Ns is the number of cells connected in
series; k is the Boltzmann’s constant (1.381×10–23
J/K); q is
the electronic charge, q=1.602×10–19
C; T is the ambient
temperature, in Kelvins.
From (1) and (2), one has
p
spvpvaV
RIV
phpvR
RIVeIII ta
spvpv +−−−=
+
)1(0. (3)
The unknown model coefficients Iph, Rs, Rp, a and I0, are
estimated by using data fitting procedure. The least square
fitting method is applied. The experimental I–V
characteristics are used. The residual function is
ii yyr ˆ−= , ),( ii xfyr β−= , (4)
with the model function f(⋅,⋅), while the estimator is given
as
( ) yXXXTT 1−
=β)
, ),( ββ
i
j
ij xfX∂
∂= . (5)
Here, i is the data index; yi is the solar cell model
current at the ith point; ŷi is the measured current at the ith
point.
The residual function for a classical model (1) is
ipv
p
sipvipvaV
RIV
ph IR
RIVeIIr ta
sipvipv
−+
−−−=
+
)1(0 (6)
The least square data fitting is performed applying
MATLAB algorithms and numerics. The initial values for the
parameters to be estimated are
,,
12
,, 00,000 scph
akT
Vq
sc
I
p
V
s II
e
II
dI
dVR
dI
dVR
oc
scoc
=
−
=== (7)
where Isc is the short-circuit current; Voc is the open-circuit
voltage.
Solar cells must be consistently evaluated and
characterized in the operating envelope. The I–V and P–V
characteristics, as well the derived parameters, are
explicitly examined and substantiated.
3.1. Crystalline Solar Cell The experiments are performed for a c-Si solar cell
under standard irradiation. The experimental I–V and P–V
characteristics are measured. The open-circuit voltage Voc is
0.548 V. The short circuit current Isc is 1.43 A. The
maximum power is 0.2 W. The voltage and current at the
maximum power are 0.275 V and 0.72 A. Applying the data
fitting procedure, the parameters are obtained using the
experimental data. We find Rs=0.34 ohm, Rp=42.3 ohm,
I0=4.79×10–7
A, Iph=1.86 A and a=1.386. The comparison
of the experimental I-V and P-V characteristics and
parametrized model are shown in Figures 3. The solar cell
model matches the experimental data.
Figure 3. Experimental (dots) and parametrized model
(solid line) I–V and P–V characteristics
3.2. Polycrystalline 40×100 mm Solar Cell We test 40×100 mm solar cells. Applying the reported
data fitting procedure using the experimental I–V and P–V
characteristics, the parameters are obtained. We have:
TechConnect Briefs 2016, TechConnect.org, ISBN 978-0-9975-1171-028
Rs=0.312 ohm, Rp=8.11 ohm, I0=2.61×10–10
A, Iph=0.618 A
and a=1.004. The comparison of the experimental and
model I-V and P-V characteristics is performed analyzing
the data depicted in Figures 4. The solar cell model matches
the experimental data. The open-circuit voltage Voc is 0.548
V, while the short circuit current Isc is 0.61 A. The
maximum power is 0.18 W, at which the voltage and
current are 0.35 V and 0.51 A.
Figure 4. Experimental (dots) and parametrized model
(solid line) I–V and P–V characteristics
3.3. Polycrystalline 20×40 mm Solar Cell A 20×40 mm polycrystalline solar cell is tested, and, the
I–V and P–V characteristics are measured. The model is
parametrized, yielding Rs=0.466 ohm, Rp=32.74 ohm,
I0=4.11×10–11
A, Iph=0.094 A and a=1.005. The I-V and P-V
characteristics are depicted in Figures 5. The open-circuit
voltage Voc is 0.548V. The short circuit current Isc is 0.091
A. The maximum power is 0.032 W with 0.43 V and 0.074
A. The consistency between the experimental data and
parametrized model is ensured.
Figure 5. Experimental (dots) and parametrized model
(solid line) I–V and P–V characteristics
3.4. Amorphous Photovoltaic Cell We study the 5×8 mm solar cells in a photovoltaic
module depicted in Figure 1. This solar module has four
solar cells in series. The experimental I–V and P–V
characteristic are measured. The open-circuit voltage is ~2
V, and, the short-circuit current is 0.35 mA. The maximum
power 0.135 mW occurs at 0.87 V and 0.15 mA. The
following parameters are found for a single-diode model
(1): Rs=0.978 ohm, Rp=1406 ohm, I0=5.46×10–14
A,
Iph=0.000322 A and a=1.31. We verify the consistency of
the solar cell model with the experimental data. The
experimental and model I-V and P-V characters are shown
in Figures 6.
Materials for Energy, Efficiency and Sustainability: TechConnect Briefs 2016 29
Figure 6. Experimental (dots) and parametrized model (1)
(solid line) I–V and P–V characteristics
The commonly used single- and multi-diode models [3,
4] must be refined. The conductivity of silicon is found
using the current density J divided by the applied electric
field E. The current density is found using the electron and
hole mobilities J=q(nµn+pµp). The resistivity is the inverse
of the conductivity, and
ρ=1/σ=1/q(nµn+pµp).
We refine conventional solar cell models, such as (1)
and others [3, 4], to a physics-consistent models. In
particular, we have
p
b
pvspvspv
DphpvR
IRIRVIII
21 ++−−= , b>0. (8)
The model is parameterized. We have Rs1=0.0000008
ohm, Rs2=15.8 ohm, Rp=2700 ohm, I0=5.3×10–13
A,
Iph=0.00094 A, a=1 and b=0.28.
The experimental and parametrized model I-V and P-V
characters are documented in Figures 7. The proposed
model (8) matches the experimental data.
Figure 7. Experimental (dots) and parametrized model
(solid line) I–V and P–V characteristics
4. CONCLUSIONS The experimental studies, analysis, evaluation and
characterization of different solar cells were performed. The
experimental I-V and P-V characteristics were measured.
The solar cell parameters are estimated. The experimental,
modeling and simulation findings were reported. The
consistent physical models were used. Our findings can be
applied to ensure the maximum power point tracking,
examine the finite energy sources, design self-sustained
power systems, etc. Due to characteristic variations and
characteristics mismatch, real-time evaluation and
adaptation are required.
REFERENCES [1] S. E. Lyshevski, “High-power density mini-scale
power generation and energy harvesting systems,”
Energy Conversion and Management, vol. 52, pp. 46-
52, 2011.
[2] S. E. Lyshevski, Mechatronics and Control of Electro-
mechanical Systems, CRC Press, Boca Raton, FL, 2016.
[3] J. A. Gow and C. D. Manning, "Development of a
photovoltaic array model for use in power-electronics
simulation studies." IEEE Proc. Electric Power
Applications, vol. 146, no. 2, pp. 193-200, 1999.
[4] R. Messenger and J. Ventre, Photovoltaic Systems
Engineering, CRC Press, Boca Raton, FL, 2010.
TechConnect Briefs 2016, TechConnect.org, ISBN 978-0-9975-1171-030